Representations of Solvable Groups

In this book Manz and Wolf concentrate on that part of representation theory which relates to solvable groups.

Olaf Manz (Author), Thomas R. Wolf (Author)

9780521397391, Cambridge University Press

Paperback, published 16 September 1993

316 pages
22.8 x 15.1 x 1.8 cm, 0.46 kg

"This is a very readable and coherent expository monograph, aimed at mathematicians and advanced students who desire a thorough knowledge of some of the main topics in the representation theory of finite solvable groups. The book features complete proofs and extensive background material." David Gluck, Mathematical Reviews

Representation theory plays an important role in algebra, and in this book Manz and Wolf concentrate on that part of the theory which relates to solvable groups. The authors begin by studying modules over finite fields, which arise naturally as chief factors of solvable groups. The information obtained can then be applied to infinite modules, and in particular to character theory (ordinary and Brauer) of solvable groups. The authors include proofs of Brauer's height zero conjecture and the Alperin-McKay conjecture for solvable groups. Gluck's permutation lemma and Huppert's classification of solvable two-transive permutation groups, which are essentially results about finite modules of finite groups, play important roles in the applications and a new proof is given of the latter. Researchers into group theory, representation theory, or both, will find that this book has much to offer.

Preliminaries
1. Solvable subgroups of linear groups
2. Solvable permutation groups
3. Module actions with large centralizers
4. Prime power divisors of character degrees
5. Complexity of character degrees
6. p-special characters.

Subject Areas: Groups & group theory [PBG]